Empirical Measures of Signal
This page is intended to provide background information relating to the traditional methods used by physicists and engineers to measure and characterize signals. In other words, by measuring quantities such as voltage, phase and time. This is in contrast to the more advanced perceptual measurements we also use which take into account how the ear and the brain perceives those signals. Obviously, in relation to human hearing, such signal inputs relate only to the audio band of hearing 50Hz – 24kHz.
Signals of any kind (audio or radio frequency – communications or radar) are normally characterized using quantities like frequency response and amplitude as displayed on a spectrum analyzer and a time varying signal versus amplitude such as displayed on an oscilloscope.
The spectrum analyzer will show the overall bandwidth or the frequency response of the signals and the amplitude of each frequency over the period of time for which the signal is being monitored or measured. The analog part of a signal processing system, such as anything from an amplifier to a cellphone call or download streaming, often introduces an increase in harmonics that were previously at a very low level. The nature of a non-linear amplifier is to increase the Total Harmonic Distortion (THD) and produce Intermodulation Distortion (IMD).
Total Harmonic Distortion
The total harmonic distortion is a measure of the total harmonic distortion output over the duration of the signal. Harmonic distortion is caused by a single sinusoid being bent out of shape. So instead of it being a pure sine wave, it perhaps shows some square wave characteristics. This causes an harmonic, which is two times the frequency of the original sine wave. Or multiple harmonics, which are multiple integers times the frequency of the original sine wave.
Intermodular distortion is created when at least two sinusoid frequencies are input to a nonlinear amplifier. The diagram above shows an example of two sine waves been input to a non-linear amplifier. This creates two additional sine waves at lower amplitude and would represent itself as distortion in the output signal. The mathematical relationship between the input and the output is shown.
High fidelity amplifiers are designed to be as linear as possible and reduce harmonic distortion to a minimum, ideally below the noise floor of the amplifier.
Some impairments are inaudible even though their amplitude may exceed the noise floor. This is known as masking. For example, a loud bash of an instrument, e.g., the symbols, generates lots of frequencies that might mask a generated impairment of noise. An error at a particular time and frequency is below the masked threshold if it is inaudible. The level difference between this and the noise floor is known as the noise-to-mask ratio.